Volkmar Welker
Professor - University of Marburg
1990: PhD in Mathematics, Universität Erlangen
1991-1999: Post-Doctoral grants and positions (MIT, Universitaet Essen, Mittag-Leffler Institute Stockholm, TU-Berlin)
1999: Professor of Mathematics, Philipps-Universität Marburg
How would you define your field of study? What is your vision about it? Which are the topics you're most passionate about?
I work in the field of Algebraic and Geometric Combinatorics. In this field combinatorial questions are translated into questions from algebra, geometry or topology and then solved using powerful machinery from these mathematical theories.
Vice versa, one employs the very same powerful machinery to translate problems from algebra, geometry and topology to combinatorial questions and then solves them using the
toolset of combinatorics.
In general, I am fascinated by the interaction of mathematical fields and I strongly believe in its potential to further the development of mathematics.
What is your teaching philosophy? What would you like to transmit to your students? How do you motivate them?
I strongly believe in learning through student - teacher interaction.Through interaction the teacher can adapt to the students' speed of learning or detect and mend their weaknesses. Nevertheless, it is indispensible to convey the message to the students, that mathematics is hard work and even the brightest minds will face frustration.In my opinion, to motivate students that have experienced frustration and failure is the toughest part of teaching mathematics.
How do you expect your experience in IMM to be? Why did you accept to teach for this project?
I have taught summer schools, mini courses etc. in Europe, USA,
Subsahran Africa and the Middle East Even though the students came from very different social, cultural and educational backgrounds they shared the passion for mathematics. I was always heartened when I experienced this passion while teaching. I expect IMM to attract the very students fascinated by mathematics and eager to absorb new theories.
Lectures
Real Rootedness and Unimodality in Discrete Geometry, MSRI (Berkeley), 2004
Selected Publications
W. Hochstättler, V. Welker: The Varchenko determinant for oriented matroids (Math. Z. to appear)
A. Conca, V. Welker: Lovasz-Saks-Schrijver ideals and coordinate sections of determinantal varieties (Algebra and Number Theory 13, 2019, 455-484, to appear)
I. Heckenberger, J. Shareshian, V. Welker: On the lattice of subracks of the rack of a finite group (Trans. Amer. Math. Soc. 372, 2019, 1407-1427)
H. Barcelo, C. Greene, A. S. Jarrah, V. Welker: Discrete cubical and path homologies of graphs (Alg. Comb. 3, 2019, 417-437)
Sarfraz Ahmad and Volkmar Welker: Partial barycentric subdivisions (Results in Mathematics 73, 2018, 22)
A. Conca, M. Kubitzke, V. Welker: Asymptotic syzygies of Stanley-Reisnerrings of iterated subdivisions (Trans. Amer. Math. Soc. 370, 2018, 1661–1691)
Appointments and Awards
1995: Heinz-Meier-Leibnitz prize from German Science Foundation ( DFG)
Advisory Board Memeber "Journal of Combinatorial Theory, Ser A" (2003-)
Postdoctoral and Research Member "Insitute Mittag-Leffler" (1991/92 and 2005)
Research Member and Research Professor MSRI (1996/97,2008,2014/15,2018/19)